Solve for $x$ and $y$ using elimination. ${2x+y = 21}$ ${-3x+y = -29}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${-2x-y = -21}$ $-3x+y = -29$ Add the top and bottom equations together. $-5x = -50$ $\dfrac{-5x}{{-5}} = \dfrac{-50}{{-5}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {2x+y = 21}\thinspace$ to find $y$ ${2}{(10)}{ + y = 21}$ $20+y = 21$ $20{-20} + y = 21{-20}$ ${y = 1}$ You can also plug ${x = 10}$ into $\thinspace {-3x+y = -29}\thinspace$ and get the same answer for $y$ : ${-3}{(10)}{ + y = -29}$ ${y = 1}$